Polarimetry methods

• 1PF: one-photon fluorescence

  • variables: (ρ, ψ).
  • defined as: given $I({\bf x},\alpha)=a_0({\bf x})+a_2({\bf x}) \cos 2\alpha +b_2({\bf x}) \sin 2\alpha$ where ${\bf x}$ is the position of the pixel and $\alpha$ the polarization angle,
  • $\rho\in [0, 180^\circ[$ (orientation) and $\psi\in [0^\circ, 180^\circ]$
  • reference: A. Kress, X. Wang, H. Ranchon, J. Savatier, H. Rigneault, P. Ferrand, S. Brasselet, Mapping the local organization of cell membranes using excitation-polarization-resolved confocal fluorescence microscopy, Biophys. J. 105, 127-136 (2013)

• CARS: coherent anti-Stokes Raman scattering

  • variables: (ρ, S₂, S₄)
  • defined as: given $\sqrt{I({\bf x},\alpha)}=a_0({\bf x})+a_2({\bf x}) \cos 2\alpha +b_2({\bf x}) \sin 2\alpha + a_4({\bf x}) \cos 4\alpha +b_4({\bf x}) \sin 4\alpha$ where ${\bf x}$ is the position of the pixel and $\alpha$ the polarization angle, $S_2({\bf x})=3\frac{\sqrt{a_2^2+b_2^2}}{2a_0}$ and $S_4({\bf x})=6\frac{\sqrt{a_4^2+b_4^2}}{a_0}\cos 4(\phi-\rho)$ where $\rho({\bf x})={\rm atan2} \frac{b_2}{a_2}$ and $\phi({\bf x})={\rm atan2} \frac{b_4}{a_4}$
  • $\rho\in [0, 180^\circ[$ (orientation), $S_2\in [0, 1]$ and $S_4\in [-1, 1]$
  • reference: J. Duboisset, P. Berto, P. Gasecka, F.Z. Bioud, P. Ferrand, H. Rigneault, S. Brasselet, Molecular orientational order probed by coherent anti-Stokes Raman scattering (CARS) and stimulated Raman Scattering (SRS) microscopy: a spectral comparative study, J. Phys. Chem. B 119, 3242–3249 (2015)

• SRS: stimulated Raman scattering

  • variables: (ρ, S₂, S₄)
  • defined as: given $I({\bf x},\alpha)=a_0({\bf x})+a_2({\bf x}) \cos 2\alpha +b_2({\bf x}) \sin 2\alpha + a_4({\bf x}) \cos 4\alpha +b_4({\bf x}) \sin 4\alpha$ where ${\bf x}$ is the position of the pixel and $\alpha$ the polarization angle, $S_2({\bf x})=3\frac{\sqrt{a_2^2+b_2^2}}{2a_0}$ and $S_4({\bf x})=6\frac{\sqrt{a_4^2+b_4^2}}{a_0}\cos 4(\phi-\rho)$ where $\rho({\bf x})={\rm atan2} \frac{b_2}{a_2}$ and $\phi({\bf x})={\rm atan2} \frac{b_4}{a_4}$
  • $\rho\in [0, 180^\circ[$ (orientation), $S_2\in [0, 1]$ and $S_4\in [-1, 1]$
  • reference: J. Duboisset, P. Berto, P. Gasecka, F.Z. Bioud, P. Ferrand, H. Rigneault, S. Brasselet, Molecular orientational order probed by coherent anti-Stokes Raman scattering (CARS) and stimulated Raman Scattering (SRS) microscopy: a spectral comparative study, J. Phys. Chem. B 119, 3242–3249 (2015)

• SHG: second-harmonic generation

  • variables: (ρ, S_SHG)
  • defined as: given $I({\bf x},\alpha)=a_0({\bf x})+a_2({\bf x}) \cos 2\alpha +b_2({\bf x}) \sin 2\alpha + a_4({\bf x}) \cos 4\alpha +b_4({\bf x}) \sin 4\alpha$ where ${\bf x}$ is the position of the pixel and $\alpha$ the polarization angle, $S_{\rm SHG}({\bf x})=-\frac{\sqrt{a_4^2+b_4^2}-\sqrt{a_2^2+b_2^2}}{2\left(\sqrt{a_4^2+b_4^2}+\sqrt{a_2^2+b_2^2}\right)}-0.65$ and $\rho({\bf x})={\rm atan2} \frac{b_2}{a_2}$
  • $\rho\in [0, 180^\circ[$ (orientation) and $S_{\rm SHG}\in [-1, 1]$

• 2PF: two-photon fluorescence

  • variables: (ρ, S₂, S₄)
  • defined as in SRS
  • reference: P. Ferrand, P. Gasecka, A. Kress, X. Wang, F.Z. Bioud, J. Duboisset, S. Brasselet, Ultimate use of two-photon fluorescence microscopy to map orientational behavior of fluorophores. Biophys. J. 106 2330–2339 (2014)

• 4POLAR 2D: 2D 4POLAR fluorescence

  • variables: (ρ, ψ)
  • $\rho\in [0, 180^\circ[$ (orientation) and $\psi\in [0^\circ, 180^\circ]$
  • reference: C. Rimoli, C. Valades Cruz, V. Curcio, M. Mavrakis, S. Brasselet, 4polar-STORM polarized super-resolution imaging of actin filament organization in cells, Nat. Comm. 13, 301 (2022)

• 4POLAR 3D: 3D 4POLAR fluorescence (beta)

  • variables: (ρ, ψ, η)
  • $\rho\in [0, 180^\circ[$ (orientation), $\eta\in [0^\circ, 90^\circ]$ and $\psi\in [0^\circ, 180^\circ]$

The colormap for ρ is hsv (and colorwheel from Colorcet for colorblind-friendly visualization).

The colormap for ψ, S₂, S₄, S_SHG is jet (and viridis for colorblind-friendly visualization).

The colormap for η is plasma.